Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions
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| Creator |
Dimakis, A.
Müller-Hoissen, F. |
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| Description |
We express AKNS hierarchies, admitting reductions to matrix NLS and matrix mKdV hierarchies, in terms of a bidifferential graded algebra. Application of a universal result in this framework quickly generates an infinite family of exact solutions, including e.g. the matrix solitons in the focusing NLS case. Exploiting a general Miura transformation, we recover the generalized Heisenberg magnet hierarchy and establish a corresponding solution formula for it. Simply by exchanging the roles of the two derivations of the bidifferential graded algebra, we recover ''negative flows'', leading to an extension of the respective hierarchy. In this way we also meet a matrix and vector version of the short pulse equation and also the sine-Gordon equation. For these equations corresponding solution formulas are also derived. In all these cases the solutions are parametrized in terms of matrix data that have to satisfy a certain Sylvester equation.
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| Date |
2019-02-09T09:31:31Z
2019-02-09T09:31:31Z 2010 |
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| Type |
Article
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| Identifier |
Bidifferential Calculus Approach to AKNS Hierarchies and Their Solutions / A. Dimakis, F. Müller-Hoissen // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 44 назв. — англ.
1815-0659 2010 Mathematics Subject Classification: 37J35; 37K10; 16E45 DOI:10.3842/SIGMA.2010.055 http://dspace.nbuv.gov.ua/handle/123456789/146356 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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